CAMPO EN REDES GSM CONOCIDO COMO LA HERRAMIENTA DRIVE TEST
CAPÍTULO 6: CONCLUSIONES Y RECOMENDACIONES
The NMR samples in this work were prepared by dissolving ~10 mg of the purified balance in 0.7 mL of the deuterated solvent of choice, giving a total concentration of ~22 mM (assuming an average molecular weight of 650). NMR peak areas were measured using peak-fitting software, which greatly reduces the error of the integration analysis. Using peak-fitting methods, NMR integration error is less than 1% for concentrations above 10 mM.i
Therefore, the error for a 1:1 folded/unfolded ratio is very small as peaks for both conformers correspond to concentrations greater than 10 mM. This error is equal to the square root of the sum of the squares of 1% and 1%, which is only 1.4% (Equation 2.1).
𝐸𝑟𝑟𝑜𝑟 [𝑓𝑜𝑙𝑑𝑒𝑑] [𝑢𝑛𝑓𝑜𝑙𝑑𝑒𝑑] = √𝐸𝑟𝑟𝑜𝑟[𝑓𝑜𝑙𝑑𝑒𝑑]2 + 𝐸𝑟𝑟𝑜𝑟 [𝑢𝑛𝑓𝑜𝑙𝑑𝑒𝑑]2 (Equation 2.1) y = -0.29x - 0.12 R² = 1.00 -1.6 -1.2 -0.8 -0.4 0.0 0.4 0.0 0.2 0.4 0.6 0.8 1.0 Δ G (kc al/m o l) equivalence of MsOH 2 →4 y = -1.24x + 0.37 R² = 1.00 -1.6 -1.2 -0.8 -0.4 0.0 0.4 0.0 0.2 0.4 0.6 0.8 1.0 Δ G (kc al/m o l) equivalence of MsOH 3 →5
However, for non-unity ratios, integration error will depend mostly on the concentration of the minor conformer as the integration error. Precise measurements of error at different concentrations could not be found. However, Rizzo et al. states that,viii “In our experience with 400–500 MHz instruments and non-refrigerated 1H-probes, qNMR may be applied to solutions with concentration as low as 1 mM if a precision of 5% is acceptable.” This observation is consistent our own observations of integration errors at 1
mM. Below 1 mM the error percentages increase rapidly above 5%, therefore, the 1 mM concentration was used as a limiting value.
Thus, for a 22 mM sample, the highest ratio that we can accurately measure is 19:1, where the minor conformer concentration is at the limiting concentration of 1 mM. This ratio will also have the highest percent error. Using equation 1 and plugging in a 1% error for the major conformer and 5% error for the minor conformer, the error in the
folded/unfolded ratio will be 5.1%.
The highest error in ΔG for the unfolded-folded conformational equilibrium is calculated using Equations 2.2 and 2.3 for the maximum ratio of 19:1. Therefore, the propagated error in ΔG (𝐸𝑟𝑟𝑜𝑟Δ𝐺) is dependent on 𝐸𝑟𝑟𝑜𝑟 [𝑓𝑜𝑙𝑑𝑒𝑑]
[𝑢𝑛𝑓𝑜𝑙𝑑𝑒𝑑]
. When the folding
ratio is 19/1, 𝐸𝑟𝑟𝑜𝑟 [𝑓𝑜𝑙𝑑𝑒𝑑] [𝑢𝑛𝑓𝑜𝑙𝑑𝑒𝑑]
is ±5.1% which is 0.0026. Plugging into equation 3 provides
a maximum 𝐸𝑟𝑟𝑜𝑟Δ𝐺 of ±0.03 kcal/mol. ∆𝐺 = 𝑅𝑇𝑙𝑛 ( [𝑓𝑜𝑙𝑑𝑒𝑑] [𝑢𝑛𝑓𝑜𝑙𝑑𝑒𝑑])
(Equation 2.2) 𝐸𝑟𝑟𝑜𝑟Δ𝐺 = 𝑅 × 𝑇 × 𝐸𝑟𝑟𝑜𝑟 [𝑓𝑜𝑙𝑑𝑒𝑑] [𝑢𝑛𝑓𝑜𝑙𝑑𝑒𝑑] (Equation 2.3) 𝐸𝑟𝑟𝑜𝑟ΔΔ𝐺= √𝐸𝑟𝑟𝑜𝑟Δ𝐺2 + 𝐸𝑟𝑟𝑜𝑟Δ𝐺2 (Equation 2.4)
CHAPTER 3
T
HECH-
ΠI
NTERACTION OFM
ETHYLE
THERS AS AM
ODEL FORC
ARBOHYDRATE-N-H
ETEROARENEI
NTERACTIONSi
iReproduced with permission from Li, P.; Parker, T. M.; Hwang, J.; Deng, F.; Smith, M. D.; Pellechia, P. J.; Sherrill, C. D.; Shimizu, K. D. Org. Lett.2014, 16, 5064. Copyright
1. Introduction
Carbohydrate recognition plays a key role in many biological processes1 such as fertilization,2 immune response,3 and inflammation.4 Thus, the study of factors that
enhance carbo-hydrate affinity and selectivity has been the focus of extensive research efforts.5 While hydrogen bonding is generally considered the primary interaction,6 CH-π interactions7 have also been cited as key contributors to carbohydrate binding.8 Interestingly, a high percentage of the CH-π interactions of carbohydrates involve heterocyclic aromatic surfaces.9 For example, the protein-sugar complex between Urtica
dioica agglutinin and the triose NAG3 contains four CH-π interactions each involving a different heterocyclic aromatic residue (Trp21, Trp23, His67 and Trp69) (Figure 3.1A).10 Thus, the goal of this work was to determine whether carbohydrates form stronger CH-π interactions with heterocyclic versus non-heterocyclic aromatic surfaces. Our strategy was to employ a small molecule model system in conjunction with computational studies to address this question. In this study, methyl ether groups were used as minimalistic models of carbohydrates. Methyl ethers can form similar CH-π interactions as those in carbohydrates as they have alkyl groups directly attached to polar oxygens (Figure 3.1B). In addition, the methyl ether groups lack hydrogen bond donating OH groups that would complicate the analysis. We found that the presence of the ether oxygen plays a key role in modulating the interaction energies and geometries of this moiety.
Figure 3.1 (A) Crystal structure of the active site of the
Urtica dioica agglutinin with a bound tri-N-acetylchitotriose (NAG3).9 The heterocyclic residues that form CH-π interactions (Trp69, Trp23, His67 and Trp21) are highlighted (PDB entry 1EHH); (B) Schematic representation of the CH- π interactions of a methyl ether group with an N-heterocyclic and non-heterocyclic aromatic ring.
Molecular torsional balances are small molecule model systems designed to measure the strength of intramolecular non-covalent interactions via shifts in a conformational equilibrium.11 Utilizing this strategy, we have recently developed a rigid bicyclic molecular balance that has been successfully applied to study a number of weak non-covalent interactions including π-π,12 CH-π,13 deuterium-π,14 and heterocyclic-π interactions.15 For this study, these balances were modified to study the CH-π interactions
of heterocyclic and non-heterocyclic aromatic surfaces (Figure 3.2). Balances 1-6 were designed with a methyl arm (OCH3 or CH2CH3) and an aromatic surface containing two,
one, or zero N-heterocyclic units that could form an intramolecular CH-π interaction. The balances were synthesized via the same modular route.11-14
Figure 3.2 (A) Schematic representation of the unfolded– folded conformational equilibrium of molecular balances 1-3
for measuring the CH-π interactions of the methyl ether group; (B) Structures of the folded conformers of molecular balances with methyl ether (1, 2, 3, and 6)and with ethyl arms (4 and 5) and their two-armed analogues (1’, 2’, 3’ and 6’) for X-crystallographic analysis.